Mathematical Modeling of Biochar Pore Descriptors from Pyrolysis Temperature: Semi-Empirical Correlations for BET Surface Area, Total Pore Volume, and Mean Pore Diameter of Lignocellulosic Feedstocks

Predicting the pore structure of lignocellulosic biochar from pyrolysis conditions without exhaustive experimental characterization remains an open challenge. We fit semi-empirical Arrhenius-type and power-law correlations linking pyrolysis temperature to SBET, VT, and d¯p by nonlinear least squares, using 45 literature records from seven open access studies (12 feedstocks, 300–800 °C). The central finding is that feedstock category, not temperature alone, dominates variance in SBET: pooled calibration explains only R2=0.199 (RMSE = 183 m2 g−1), whereas feedstock-stratified fitting recovers accuracy (e.g., RMSE = 43.6 m2 g−1 for grasses, a within-study estimate from a single source). The Arrhenius and power-law forms are statistically indistinguishable (ΔAIC<2); the Arrhenius form is adopted for physical interpretability. Pooled fits reach R2=0.691 (VT) and 0.563 (d¯p). Leave-one-study-out cross-validation (RMSE = 184 m2 g−1) confirms that reliable prediction requires calibration data within the target feedstock category. The correlations are descriptive tools valid within their calibration envelope, not general predictive models. Estimation uses no machine learning; a benchmark against OLS and random forest models confirms that greater flexibility improves in-sample fit but not out-of-sample generalization.